1. Field of the Invention
The present invention relates to communication of digital signals, more particularly to a method and a device for transmission and/or reception of digital signals using diversity (e.g. Multiple Description Coding—MDC) to overcome channel impairments, as well as to the signals themselves and a network for transmitting and receiving the signals
2. Description of the Related Technology
A new family of communication services involving the delivery of image data over bandwidth limited and error prone channels as packet networks and wireless links has emerged in the last few years. In order to increase the reliability over these types of channels, diversity is commonly resorted to, besides error correction techniques. Multiple Description Coding (MDC) has been introduced to efficiently overcome channel impairments over diversity-based systems allowing decoders to extract meaningful information from a subset of a bit-stream.
In his PhD. Thesis, which can be found in electronic format on http://lcavwww.epfl.ch/˜goyal/Thesis/, Vivek K. Goyal offers an overview of MDC in general and achievable rate-distortion regions. The focus of previous research was laid on finding the optimal achievable rate-distortion regions and their boundaries, as described in L. Ozarow, “On a source coding problem with two channels and tree receivers,” Bell Syst. Tech. J., vol. 59, pp. 1909-1921, 1980, and in A. A. El Gamal and T. M. Cover, “Achievable rates for multiple descriptions,” IEEE Trans. Inform. Th., vol. IT-28, no. 6, pp. 851-857, 1982. This is followed by the design of practical compression systems to meet these theoretical boundaries. Examples include methods based on quantization as described in V. A. Vaishampayan, “Design of multiple description scalar quantizers,” IEEE Trans. Inform. Th., vol. 39, no. 3, pp. 821-834, 1993, and in V. A. Vaishampayan and J. Domaszewicz, “Design of entropy-constrained multiple description scalar quantizers,” IEEE Trans. Inform. Theory, vol. 40, no. 1, pp. 245-250, 1994, and methods based on multiple description transform as described in J. Batllo and V. Vaishampayan, “Asymptotic performance of multiple description transform codes,” IEEE Trans. Inform. Theory, vol. 43, no. 2, pp. 703-707, 1997, and in V. Goyal, J. Kovacevic, R. Arean, and M. Vetterli, “Multiple description transform coding of images,” Proc. IEEE Int. Conf Image Proc. ICIP'98, pp. 674-678, 1998. A design of Multiple Description Scalar Quantizers (MDSQ) is pioneered in V. A. Vaishampayan, “Design of multiple description scalar quantizers,” IEEE Trans. Inform. Th., vol. 39, no. 3, pp. 821-834, 1993 under an assumption of fixed length codes and fixed codebook sizes. Significant improvements are achieved in V. A. Vaishampayan and J. Domaszewicz, “Design of entropy-constrained multiple description scalar quantizers,” IEEE Trans. Inform. Theory, vol. 40, no. 1, pp. 245-250, 1994 where the design of the quantizers is subject to the constraint of a given entropy, and not of a given codebook size.
In order to achieve robust communication over unreliable channels the MDC system has to deliver highly error-resilient bit-streams characterised by a corresponding high level of redundancy. Additionally, a fine grain scalability of the bit-stream is a desirable feature for bandwidth varying channels. A system conceived so as to meet these requirements is described in T. Guionnet, C. Guillemot, and S. Pateux, “Embedded multiple description coding for progressive image transmission over unreliable channels,” Proc. IEEE Int. Conf Image Proc., ICIP 2001, pp. 94-97, 2001, where a progressive MDC algorithm is based on Multiple Description Uniform Scalar Quantizers (MDUSQ). Moreover, for a high level of redundancy and for low bit-rates, the approach of this document outperforms the embedded MDC algorithm based on a polyphase transform as proposed in W. Jiang and A. Ortega, “Multiple description coding via polyphase transform and selective quantization,” Proc. SPIE Int. Conf Visual Comm. Image Proc., VCIP'99, San Jose, USA, pp. 998-1008, 1999.
The system proposed in V. A. Vaishampayan, “Design of multiple description scalar quantizers,” IEEE Trans. Inform. Th., vol. 39, no. 3, pp. 821-834, 1993, relies on the ability to design scalar quantizers with nested thresholds. A source signal or input signal, generally called “a source”, represented by a random process {Xn, nεz30} with zero mean and variance σX2 is quantized by side quantizers QSm:R→{0,1, . . . ,K−1}, m being a value between 1 and the number of side quantizers available, for example m=1, 2, and K being the number of quantization intervals of a side quantizer for a quantization level. In the example given with two side quantizers, each of the two quantizers outputs an index qkm,kεz+ for a quantization level, which indexes can be separately used to estimate the source sample. A reconstruction where QSm(x)=qkm must be the centroid of the cell or quantization interval QSm−1(qkm). If both indices QC1(x)=qk1 and QS2(x)=qk2 are received, the reconstruction is the centroid of the intersection QC−1(qk1,qk2)=QS1−1(qk1),∩QS2−1(qk2) represented by the central inverse quantizer. The number of diagonals covered in the index assignment matrix triggers the redundancy between the two descriptions, as described in V. A. Vaishampayan, “Design of multiple description scalar quantizers,” IEEE Trans. Inform. Th., vol. 39, no. 3, pp. 821-834, 1993.
Quantization methods based on embedded scalar quantizers are previously proposed in the literature—see for e.g. D. Taubman and M. W. Marcellin, JPEG2000—Image Compression: Fundamentals, Standards and Practice. Hingham, Mass.: Kluwer Academic Publishers, 2001. In embedded quantization, the partition cells or quantization intervals at higher quantization rates are embedded in the quantization intervals at lower rates. A quantization rate relates to the number of quantization intervals at a quantization level. A set of embedded side quantizers QSm,0, QSm,1, . . . , QSm,P with m=1,2 the number of side quantizers, and P+1 the number of quantization levels, and a set of embedded central quantizers QC0, QC1, . . . , QCP where QCP−1(qk1,qk2)=QS1,p−1(qk1)∩QS2,p−1(qk2) for any quantization level p, 0≦p≦P are assumed. The number of quantization levels may be freely selected e.g. seven or more or ten or more levels. The quantization intervals of any quantizer QSm,p and QCp are embedded in the quantization intervals of the quantizers QSm,P, QSm,P−1, . . . , QSm,P+1 and QCP, QCP−1, . . . , QCP+1 respectively. It is considered that the quantizer at level p (e.g. QSm,p) is finer than the quantizer at level p+1 (e.g. QSm,p+1) if at least one of the quantization intervals of the quantizer at level p+1 is split into at least two quantization intervals at level p.
The number of side quantization intervals of the lowest-rate quantizer QSm,P is denoted by N and the number of quantization intervals in which an arbitrary side quantization interval Skm,p of QSm,p is divided is denoted by Lk. The maximum number of intervals in which any side quantization interval Skm,p is partitioned over all quantization levels is denoted by Np, with Lk≦Np for any k. Starting from the lowest-rate quantizer QSm,P, each side quantization interval Skpm,P, 0≦kp<N is divided into a number of Lkp quantization intervals Skp,kp−1m,P−1,0≦kP−1<Lkp of QSm,P−1. In general, for each side-quantizer QSm,p one associates to any xεSkp,kp−1, . . . , kpm,p the quantizer index kp, kp−, . . . ,kp. This allows to obtain the indices of lower rate quantization by leaving aside components of higher rate quantization, similar to the uniform embedded scalar quantizers as described in D. Taubman and M. W. Marcellin, JPEG2000—Image Compression: Fundamentals, Standards and Practice. Hingham, MA: Kluwer Academic Publishers, 2001.